Movie Moves for Knotted Surfaces with Markings

TL;DR

This paper extends Carter and Saito's movie theorem to marked knotted surfaces, incorporating link Floer homology markings and defining new equivalence relations to handle isotopy complexities.

Contribution

It introduces a marked analogue of the movie theorem tailored for surfaces with link Floer homology markings, addressing isotopy complications with new equivalence relations.

Findings

Established a marked version of Carter and Saito's movie theorem.

Defined three equivalence relations for marked surfaces.

Worked over equivalence classes of marked surfaces for generalization.

Abstract

We present a marked analogue of Carter and Saito's movie theorem. Our definition of marking was chosen to coincide with the markings that arise in link Floer homology. In order to deal with complications arising from certain isotopies, we define three equivalence relations for marked surfaces and work over an equivalence class of marked surfaces when providing our generalization of Carter and Saito's movie theorem.